Brownian Motion and Thermophoretic Effect on Thin-Film Copper Nanofluid Flow over a Stretching Sheet

The rapid expansion of industrial and engineering activities has introduced new and complex heat transfer challenges. Many modern systems operate under conditions that require high thermal loads, thereby demanding effective heat management strategies. To address this, advancements in nanotechnology have been employed to improve the thermal performance of conventional fluids. In this study, nanoparticles were uniformly dispersed within a base fluid to enhance its thermal conductivity, leading to a significant improvement in convective heat transfer rates. The mathematical formulation of the problem involved the continuity, momentum, energy, and concentration equations, which were expressed as partial differential equations (PDEs). Through the application of similarity transformations, these equations were reduced to a system of nonlinear ordinary differential equations (ODEs). The transformed equations were then solved numerically using the collocation method (BVP4C) implemented in MATLAB, a robust solver known for its stability and accuracy in boundary value problems. The obtained results demonstrated that the presence of nanoparticles considerably improves the heat transfer characteristics of the fluid by enhancing both the temperature and velocity distributions. These findings provide valuable insights for the development of advanced nanofluids with optimized thermal properties. Such fluids hold great potential for use as efficient coolants in a wide range of applications, including electronic device cooling, automotive thermal systems, air conditioning units, and power generation equipment, where enhanced thermal management is essential for operational reliability and energy efficiency.